
48 Fundamentals of Sensors for Engineering and Science
moves upward and the other leg downward). Thus, the total torque equals
2F
C
h, where h is the lateral distance between the two legs of the tube. Not-
ing that the mass flow rate of the fluid, ˙m = ρUA, the mass flow rate can
be related to the frequency by
˙m =
T
2Lhω
. (2.49)
This can be expressed in terms of the twist displacement angle, θ
tw
, by
noting that θ
tw
= T/K, where K is the elastic stiffness of the tube. Thus,
Equation 2.49 becomes
˙m =
Kθ
2Lhω
. (2.50)
The twist displacement angle usually is small, such that sin θ ' θ '
∆y/(h/2), where ∆y is the vertical displacement normal to the plane of
the tube